What is the extreme f(x)=6x+8/x ?

The extreme f(x)=6x+8/x is Maximum(-2/(sqrt(3)),-8sqrt(3)),Minimum(2/(sqrt(3)),8sqrt(3))

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extreme f(x)=6x+8/x

extreme points

f (x) = 6 x + \frac{8}{x}

Maximum (- \frac{2}{3}, - 83), Minimum (\frac{2}{3}, 83)

Solution steps

f^{'} (x) = 6 - \frac{8}{x ^{2}}

Find intervals:

Increasing

: - \infty < x < - \frac{2}{3},

Decreasing

: - \frac{2}{3} < x < 0,

Decreasing

: 0 < x < \frac{2}{3},

Increasing

: \frac{2}{3} < x < \infty

Plug

x = - \frac{2}{3}

into

6 x + \frac{8}{x} : - 83

Maximum (- \frac{2}{3}, - 83)

Plug

x = \frac{2}{3}

into

6 x + \frac{8}{x} : 83

Minimum (\frac{2}{3}, 83)

Maximum (- \frac{2}{3}, - 83), Minimum (\frac{2}{3}, 83)

x^{\frac{3}{5}}

+ \frac{1}{4 x - 8}

f (x) = \frac{8.7 x + 0.2}{x ^{2} - 4.5 x + 7.5}

f (t) = \frac{e ^{t}}{t ^{2} + 1}, (0, 3)

f (x) = 5 x^{3} - 5 x^{2} - 5 x + 7

What is the extreme f(x)=6x+8/x ?
The extreme f(x)=6x+8/x is Maximum(-2/(sqrt(3)),-8sqrt(3)),Minimum(2/(sqrt(3)),8sqrt(3))